What is prime and composite numbers?

Why it matters

Primes are the building blocks of every other whole number: every composite breaks down into a unique product of primes (its prime factorization). This sets up greatest common factor, least common multiple, and simplifying fractions, all of which dominate Grade 4-6 math.

Worked example

Is 12 prime or composite? Is 13 prime or composite?

1. 1

   Start with 12. List its factors, all the whole numbers that divide 12 evenly.

   A factor is a number that fits into another number a whole number of times. Test 1, 2, 3, 4, ... up to 12.

2. 2

   Factors of 12: 1, 2, 3, 4, 6, 12. That’s 6 factors total.

   1 × 12 = 12, 2 × 6 = 12, 3 × 4 = 12. Each multiplication pair gives two factors.

3. 3

   12 has more than two factors, so 12 is COMPOSITE.

   Anything with factors beyond just 1 and itself is composite.

4. 4

   Now 13. Try to find factors: 1 divides 13 (1 × 13 = 13). 2? No (13 is odd). 3? No (13 ÷ 3 isn’t whole). 4? No. 5? No. 6? No. Keep going. None work except 1 and 13 itself.

   You only need to test divisors up to √13 ≈ 3.6, so really just 2 and 3, a Grade 4 shortcut to learn later.

5. 5

   13 has exactly two factors (1 and 13), so 13 is PRIME.

Common mistakes

• •Calling 1 a prime number. 1 has only ONE factor (itself), not two, so by definition it’s neither prime nor composite.
• •Calling 2 composite because "all even numbers are composite." 2 is actually the ONLY even prime: its only factors are 1 and 2.
• •Stopping the factor search too early, e.g. deciding 91 is prime because 2, 3, and 5 don’t divide it, missing that 91 = 7 × 13.
• •Confusing factors with multiples. Factors of 12 are 1, 2, 3, 4, 6, 12. Multiples of 12 are 12, 24, 36, 48, and so on. They are completely different sets.

How Briveli teaches prime and composite numbers

Briveli teaches prime and composite numbers in Grade 4 with a build-up that starts from factor pairs and arrays, then moves into prime factorization in Grade 5 and 6, used directly for greatest common factor and least common multiple problems.